In tomography, multiple methods are utilized for image reconstruction purposes. Differing methods have advantages and disadvantages in terms of quality, computational efficiency, and the like.
One such method is called Filtered Backprojection (FBP). FBP methods are generally seen as simple and fast methods for use in image reconstruction. Such methods are commonly used in Nuclear Medicine, x-ray computed tomography (CT) or even magnetic resonance imaging (MRI) applications which utilize certain special data acquisition methods. FBP algorithms generally are Fourier transform-based methods that control noise by using window functions and carefully designed cut-off frequencies. In implementation, raw image data is sent through a high pass filter (typically a ramp filter) to provide image sharpness. Then, a backprojection step assigns all the filtered data back to the image in order to reconstruct a higher quality image.
One advantage of FBP methods is that they are seen as being very fast. However, disadvantages occur because FBP generally requires a very uniform sampling of the object to be imaged. Additionally, FBP methods are prone to noise which is oftentimes difficult to control. In fact, currently in nuclear medicine applications, e.g., positron emission tomography (PET) and single photon emission computed tomography (SPECT), FBP has become disfavored because of the excess image noise.
Another common type of method used for image reconstruction may be referred to as an iterative algorithm method. Compared with FBP methods, iterative methods generally produce images which are less noisy, even when the iterative algorithm (e.g., an iterative Landweber algorithm) does not model the projection noise or does not model the projection noise correctly. As a result, FBP methods have gradually been replaced by iterative image reconstruction algorithms, among which the maximum-likelihood expectation-maximization (ML-EM) and ordered-subsets expectation-maximization (OS-EM) algorithms are the most popular.
Iterative algorithms may also utilize prior information for future processing iterations. Such a use can assist in reducing noise, reducing modeling error, etc., in order to provide higher quality images. Additionally, in an iterative technique, raw data sampling does not have to be uniform. Such functionalities are generally not possible when using FBP techniques.
One disadvantage to iterative algorithm methods is that they are generally much slower than FBP methods. For example, when reconstructing an image, an iterative algorithm may run 50-100 iterations, and for each iteration, the processing cost is generally twice as much as the computer processing cost of a single FBP reconstruction. As such, if a user implements 100 iterations, the image reconstruction may be as much as 200 times slower, however, it generally produces better images. For certain tomography applications this may be acceptable. However, when implementing some imaging techniques, such as a CT scan, the raw data received is too large to implement such an iterative algorithm.
Another disadvantage of iterative methods is that the image produced generally cannot have a shift-invariant property. In other words, the point spread function or point response function is not stationary. With FBP, the point response function or point spread function is shift invariant. In implementation, this means that if you have a point, a source, or a lesion in the body, depending on the body location of the source, an FBP method can produce the same image regardless of scan location, but iterative methods produce different images corresponding to the location of the source. This is especially true if the lesion is on the edge of the image area.
Other approaches to provide for more efficient and high quality image reconstruction may be characterized as hardware approaches. For example, some methods utilize a graphic processing unit (GPU) or parallel processing techniques in an effort to perform multiple tasks simultaneously. These approaches may utilize multiple computers and processing devices (sometimes involving 100+ processors) in order to process large amounts of raw data. However, such approaches tend to be expensive or difficult to implement.